3 Answers
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The reason that roasted garlic tastes so much milder than raw garlic is that it contains a sulfur compound called allicin, which roasting breaks down. Allicin is primarily what gives garlic its pungency. Technically, raw garlic mostly contains a compound called allin, which reacts with the allinase enzyme to produce the allicin, and this reaction is greatly accelerated when garlic is "distressed", i.e. crushed or cut.

Ginger contains no allicin, so you're certainly not going to get an identical reaction. What ginger does contain are two types of oil called gingerols and shogaols, which are primarily what gives ginger its pungency. Cooking converts these into another compound called zingerone, which is far less pungent (it's described as "spicy-sweet"). It's actually slightly more complicated; the gingerols also convert into shogaols through cooking, and the shogaols are actually more pungent (160,000 SHU vs. 60,000), but on the whole, the ginger does become milder.

It will not become perfectly sweet as garlic does, just less pungent and more aromatic. In fact, cooked (roasted) ginger tastes much like dried ginger; many of the same reactions happen during drying as during cooking.

So yes, you can try roasting ginger if you want it to be milder, but don't expect to be able to eat the whole root by itself if you don't already love the taste of ginger. It doesn't do exactly the same thing that garlic does, it's just a little similar.

It's hard to find good references online, although you can find a lot of this in McGee. For more information you can try:

Slicing peeled ginger thin on the bias (with the grain) and roasting it until the slices are gently browned (I do this under a broiler) will result in a pleasant caramelization that is not present in raw ginger. Don't let it go too long, experiment a bit to see how you like it.